二维土质边坡稳定可靠性分析分层离散随机场矩方法
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摘要
针对边坡稳定可靠性涉及多参数相关且具有空间变异性、极限状态方程非显式等难题,建立土质边坡稳定可靠性分析的分层离散随机场矩法。基于局部平均理论,根据土性参数的竖向分层特性,将层内参数简化为随机变量,不同层的参数通过方差函数体现其竖向空间变异性,提出高效的土性参数分层离散随机场模型,可有效模拟土性参数的竖向变异性以及多参数相关性。将边坡稳定可靠性功能函数简化为土性参数的降维近似函数,采用点估计的高阶矩法,建立土质边坡稳定可靠性分析的离散随机场矩法。算例分析结果与MCS以及多重随机响应面法结果高度一致,验证了本文方法的高效、简捷与合理。
In order to overcome the difficulties such as the spatial variability of correlated multi-parameters and the implicity of limit state equations in the reliability analysis of soil slope stability,a moment method based on the layered discrete random field of soil parameters was presented. According to the local average process theory and the vertical variation of soil parameters,a layered discrete random field model of soil parameters was proposed,in which the soil parameters within each soil layer are regarded as random variables and the spatial variability of the soil parameters in adjacent layers is described by variance functions. The reliability function of soil slope stability was simplified as a reduced-dimension function of soil parameters,and the reliability of the slope stability was calculated by the four-order moment method. Comparisons among the proposed method,MCS and the multi-random response surface method using slope examples were performed and a good agreement among them was illustrated.
In order to overcome the difficulties such as the spatial variability of correlated multi-parameters and the implicity of limit state equations in the reliability analysis of soil slope stability,a moment method based on the layered discrete random field of soil parameters was presented. According to the local average process theory and the vertical variation of soil parameters,a layered discrete random field model of soil parameters was proposed,in which the soil parameters within each soil layer are regarded as random variables and the spatial variability of the soil parameters in adjacent layers is described by variance functions. The reliability function of soil slope stability was simplified as a reduced-dimension function of soil parameters,and the reliability of the slope stability was calculated by the four-order moment method. Comparisons among the proposed method,MCS and the multi-random response surface method using slope examples were performed and a good agreement among them was illustrated.
引文
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[20]蒋水华,李典庆,曹子君,等.考虑参数空间变异性的边坡系统可靠度分析[J].应用基础与工程科学学报,2014,22(5):841-855.(JIANG Shuihua,LI Dianqing,CAO Zijun,et al.System reliability analysis of slopes considering spatial variability of soil properties[J].Chinese Journal of Basic Science and Engineering,2014,22(5):841-855.(in Chinese))
[2]LUMP P.The variability of natural soils[J].Canadian Geotechnical Journal,1966,3(2):74-97.
[3]VANMARCKE E H.Random fields:analysis and synthesis[M].[S.l.]:World Scientific,2010:189-205.
[4]VANMARCKE E H.随机场:分析与综合[M].陈朝晖,范文亮,译.北京:高等教育出版社,2017:153-172.(VANMARCKE E H.Random fields:analysis and synthesis[M].Translated by CHEN Zhaohui,FAN Wenliang.Higher Education Press,2017:153-172.(in Chinese))
[5]EI-RAMLY H.Probabilistic analyses of landslide hazards and risks:bridging theory and practice[Ph.D.Thesis][D].Edmonton,Alta:University of Alberta,2001.
[6]SPANOS P D,BEER M,RED-HORSE J.Karhunen-Loéve expansion of stochastic processes with a modified exponential covariance kernel[J].Journal of Engineering Mechanics,2007,133(7):773-779.
[7]EVANS D H.An application of numerical integration techniques to statistical toleraucing[J].Technometrics,1967,9(3):441-456.
[8]ROSENBLUETH E.Point estimates for probability moments[J].Proceedings of the National Academy of Sciences,1975,72(10):3 812-3 814.
[9]ZHAO Y G,ONO T.New point estimates for probability moments[J].Journal of Engineering Mechanics,2000,126(4):433-436.
[10]范文亮,李正良,王承启.多变量函数统计矩的点估计法性能比较[J].工程力学,2012,29(11):1-11.(FAN Wenliang,LIZhengliang,WANG Chengqi.Comparison of point estimate methods for probability moments of multivariate function[J].Engineering Mechanics,2012,29(11):1-11.(in Chinese))
[11]李云贵,赵国藩.结构可靠度的四阶矩分析法[J].大连理工大学学报,1992,32(4):455-459.(LI Yungui,ZHAO Guofan.Four order method of structural reliability[J].Journal of Dalian University of Technology,1992,32(4):455-459.(in Chinese))
[12]ZHAO Y G,ONO T.Moment methods for structural reliability[J].Structural Safety,2001,23(1):47-75.
[13]ZHAO Y G,LU Z H.Fourth-moment standardization for structural reliability assessment[J].Journal of Structural Engineering,2007,133(7):916-924.
[14]ZHAO Y G,ONO T.On the problems of the fourth moment method[J].Structural Safety,2004,26(3):343-347.
[15]DAVIS R A,LII K S,POLITIS D N.Remarks on a multivariate transformation[M].New York:Springer,2011:49-51.
[16]LI H S,LüZ Z,YUAN X K.Nataf transformation based point estimate method[J].Chinese Science Bulletin,2008,53(17):2 586-2 592.
[17]ONO T,IDOTA H.Development of high-order moment standardization method into structural design and its efficiency[J].Journal of Structural and Construction Engineering,1986,365:40-47.
[18]KENDALL M,STUART A,ORD J K.Kendall's advanced theory of statistics[M].New York:Oxford University Press,1987.
[19]黄景华,陈朝晖,莫玻,等.参数特性及分布形式对边坡稳定可靠性的影响分析[J].四川大学学报:工程科学版,2014,46(3):23-30.(HUANG Jinghua,CHEN Zhaohui,MO Bo,et al.Influence analysis of characteristics and distribution types of soil parameters on slope reliability[J].Journal of Sichuan University:Engineering Science,2014,46(3):23-30.(in Chinese))
[20]蒋水华,李典庆,曹子君,等.考虑参数空间变异性的边坡系统可靠度分析[J].应用基础与工程科学学报,2014,22(5):841-855.(JIANG Shuihua,LI Dianqing,CAO Zijun,et al.System reliability analysis of slopes considering spatial variability of soil properties[J].Chinese Journal of Basic Science and Engineering,2014,22(5):841-855.(in Chinese))